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Poulation growth: logistic function
Logistic growth

Input data

Year 1

Year 2

Year 3

Year of interest

Population 1

Population 2

Population 3

Output data

Predicted population's size

Description

Given the observed populations in three known and equidistant years, determines the logistic function applied to the period and predicts the future population through this function.

Logistic Growth

Calculation Methods

Logistic growth

This method uses the data from three known years to determine the logistic curve of the population and predict future population. The formula used is:

Py=K1+ea+b(ty−t1)P_y = \dfrac{K}{1 + e ^ {a + b(t_y - t_1)}}

where:

  • KK is the carrying capacity, calculated using:

    K=2P1P2P3−(P1+P3)P22P1P3−P22 K = \dfrac{2P_1P_2P_3 - (P_1 + P_3)P_2^2}{P_1P_3 - P_2^2}

  • aa and bb are constants determined from the given data.

Input and Output Parameters

ParameterDefault UnitsDescription
Year 1-First year of observation
Year 2-Second year of observation
Year 3-Third year of observation
Year of interest-Year for which the prediction is made
Population 1-Population observed in Year 1
Population 2-Population observed in Year 2
Population 3-Population observed in Year 3
Predicted population's size-Estimated population for the year of interest

References

  • VIANNA, Marcos Rocha. Produção, Reservação e Distribuição de Água. e-book. Belo Horizonte: Bloom, 2021.